(3p-1)(8p+4)=

Solution for (3p-1)(8p+4)= equation:

Simplifying
(3p + -1)(8p + 4) = 0

Reorder the terms:
(-1 + 3p)(8p + 4) = 0

Reorder the terms:
(-1 + 3p)(4 + 8p) = 0

Multiply (-1 + 3p) * (4 + 8p)
(-1(4 + 8p) + 3p * (4 + 8p)) = 0
((4 * -1 + 8p * -1) + 3p * (4 + 8p)) = 0
((-4 + -8p) + 3p * (4 + 8p)) = 0
(-4 + -8p + (4 * 3p + 8p * 3p)) = 0
(-4 + -8p + (12p + 24p2)) = 0

Combine like terms: -8p + 12p = 4p
(-4 + 4p + 24p2) = 0

Solving
-4 + 4p + 24p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + p + 6p2) = 0

Factor a trinomial.
4((-1 + -2p)(1 + -3p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -2p)' equal to zero and attempt to solve:

Simplifying
-1 + -2p = 0

Solving
-1 + -2p = 0

Move all terms containing p to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2p = 0 + 1
-2p = 0 + 1

Combine like terms: 0 + 1 = 1
-2p = 1

Divide each side by '-2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 2
Set the factor '(1 + -3p)' equal to zero and attempt to solve:

Simplifying
1 + -3p = 0

Solving
1 + -3p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3p = 0 + -1
-3p = 0 + -1

Combine like terms: 0 + -1 = -1
-3p = -1

Divide each side by '-3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
Solution
p = {-0.5, 0.3333333333}